Contributions to the study of Anosov Geodesic Flows in Non-Compact\n Manifolds

2018/10/23 by Ítalo Melo, Sergio Romaña, Melo, Ítalo +1 · 1 citation
Computer Science · Mathematics · #37D40 53A10 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1810.09998

openalex publication_date 2018/10/23 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that if the geodesic flow of a compact or\nnon-compact complete manifold without conjugate points is of the Anosov type,\nthen the average of the integral of the sectional curvature along the geodesic\nis negative and away from zero from a uniform time. Moreover, in dimension two,\nif the manifold has no focal points, then this condition is sufficient to\nobtain that the geodesic flow is of Anosov type. This sufficient condition will\nalso be used to construct new examples of non-compact surfaces whose geodesic\nflow is of the Anosov type.\n

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